Figures 3 summarize the temperature variations of
the in-plane transport properties in [Ca\(_2\) CoO\(_3\) ]\(_{0.62}\) [CoO\(_2\) ].
Hereafter we use an abbreviated form like \(\rho _a (=\rho _{aa})\)  for the resistivity measured along the \(a\) -axis direction.
Overall behaviors are well reproduced compared with the earlier reports in which the
transport coefficients are measured with no distinction among the in-plane directions [1]}.
In addition, the thermopower measured along the \(b\)  axis \(Q_b\)  is larger than
that along the \(a\)  axis \(Q_a\) , consistent with recent theoretical calculation [2]}.
At low temperature below \(\sim 100\)  K,
the resistivity shows an insulating behavior while the thermopower seems to be metallic,
which are discussed in terms of carrier localization [3]}, pseudogap opening [4]}, or quantum criticality [5]}.
Near room temperature,
the thermopower shows a temperature-independent behavior with
a relatively large value of \(Q\simeq 130\)  \(\mu \) V/K,
quantitatively explained by the
extended Heikes formula of

Q=-kBe(g3g4y1-y
),


where \(k_B\)  is the Boltzmann coefficient, \(e\)  the elementary charge,
\(g_3\)  and \(g_4\)  the spin and orbital degeneracies of Co\(^{3+}\)  and Co\(^{4+}\)  ions,
respectively, and
\(y\)  the Co\(^{4+}\)  (hole) concentration [6]}.
Enhancement of the thermopower above room temperature may be possibly
attributed to a small spin-state change near \(T\simeq 380\)  K [7]},
above which the degeneracy ratio \(g_3/g_4\)  may vary with temperature.
At this temperature, a small anomaly has been observed in several quantities such as the resistivity, magnetic susceptibility, heat capacity, and lattice constants [1]}, [9]}, [7]}.
On the other hand, the magnitude of the resistive anomaly may be sample-dependent [11]} and is not resolved in the present samples.
Although the present measurements are limited below 600 K,
the increase of thermopower may continue up to 1000 K
according to high-temperature transport experiments in this compound [12]}.
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